Micromachined rate and acceleration sensor

ABSTRACT

A sensor (10) is disclosed for measuring the specific force and angular rotation rate of a moving body and is micromachined from a silicon substrate (16). First and second accelerometers (32a and b) are micromachined from the silicon substrate (16), each having a force sensing axis (38) and producing an output signal of the acceleration of the moving body along its force sensing axis (38). The first and second accelerometers (32a and b) are mounted within the substrate (16) to be moved along a vibration axis (41). The first and second accelerometers (32a and b) are vibrated or dithered to increase the Coriolis component of the output signals from the first and second accelerometers (32a and b). A sinusoidal drive signal of a predetermined frequency is applied to a conductive path (92) disposed on each of the accelerometers. Further, magnetic flux is directed to cross each of the conductive paths (92), whereby the interaction of the magnetic flux and of the drive signal passing therethrough causes the desired dithering motion. A link (72) is formed within the silicon substrate (16) and connected to each of the accelerometers (32a and b), whereby motion imparted to one results in a like, but opposite motion applied to the other accelerometer (32). Further, a unitary magnet (20) and its associated flux path assembly direct and focus the magnetic flux through the first and second accelerometers (32a and b) formed within the silicon substrate (16).

This is a Division of U.S. application Ser. No. 07/653,533, filed Feb.8, 1991 now U.S. Pat. No. 5,241,861.

FIELD OF THE INVENTION

This invention relates to an apparatus and method for determining therate of angular rotation of a moving body and, in particular, adapted tobe formed, e.g. micromachined, from a silicon substrate.

REFERENCE TO RELATED APPLICATIONS

Reference is made to the following commonly assigned, copending patentapplications:

1) entitled "Monolithic Accelerometer" U.S. Ser. No. 07/377,785, filedJuly 6, 1989 in the name of Brian L. Norling;

2) entitled "Accelerometer with Co-Planar Push-Pull Force Transducers",U.S. Ser. No. 07/316,399, filed Feb. 27, 1989 in the name of MitchNovack;

3) entitled "Coriolis Inertial Rate and Acceleration Sensor", filed Feb.8, 1991, U.S. Ser. No. 653,535 in the name of Rand H. Hulsing II;

4) entitled "Translational Accelerometer with Motion Constraints", filedNov. 5, 1990, U.S. Ser. No. 609,248, in the names of B. Norling and S.Becka.

5) entitled "Torque Coil Stress Isolator" U.S. Ser. No. 07/569,398, byS. Foote.

BACKGROUND OF THE INVENTION

The rate of rotation of a moving body about an axis may be determined bymounting an accelerometer on a frame and dithering it, with theaccelerometer's sensitive axis and the direction of motion of the frameboth normal to the rate axis about which rotation is to be measured. Forexample, consider a set of orthogonal axes X, Y and Z oriented withrespect to the moving body. Periodic movement of the accelerometer alongthe Y axis of the moving body with its sensitive axis aligned with the Zaxis results in the accelerometer experiencing a Coriolis accelerationdirected along the Z axis as the moving body rotates about the X axis. ACoriolis acceleration is that perpendicular acceleration developed whilethe body is moving in a straight line, while the frame on which it ismounted rotates. This acceleration acting on the accelerometer isproportional to the velocity of the moving sensor body along the Y axisand its angular rate of rotation about the X axis. An output signal fromthe accelerometer thus includes a DC or slowly changing component orforce signal F representing the linear acceleration of the body alongthe Z axis, and a periodic component or rotational signal Ω representingthe Coriolis acceleration resulting from rotation of the body about theX axis.

The amplitude of that Coriolis component can be produced by vibratingthe accelerometer, causing it to dither back and forth along a lineperpendicular to the input axis of the accelerometer. Then, if the frameon which the accelerometer is mounted is rotating, the Coriolisacceleration component of the accelerometer's output signal will beincreased proportional to the dither velocity. If the dither amplitudeand frequency are held constant, then the Coriolis acceleration isproportional to the rotation rate of the frame.

The linear acceleration component and the rotational componentrepresenting the Coriolis acceleration may be readily separated by usingtwo accelerometers mounted in back-to-back relationship to each otherand processing their output signals by sum and difference techniques. InU.S. Pat. No. 4,510,802, assigned to the assignee of this invention, twoaccelerometers are mounted upon a parallelogram with their input axespointing in opposite directions. An electromagnetic D'Arsonval coil ismounted on one side of the parallelogram structure and is energized witha periodically varying current to vibrate the accelerometers back andforth in a direction substantially normal to their sensitive or inputaxes. The coil causes the parallelogram structure to vibrate, ditheringthe accelerometers back and forth. By taking the difference between thetwo accelerometer outputs, the linear components of acceleration aresummed. By taking the sum of the two outputs, the linear componentscancel and only the Coriolis or rotational components remain.

U.S. Pat. No. 4,5,801, commonly assigned to the assignee of thisinvention, describes the processing of the output signals of twoaccelerometers mounted for periodic, dithering motion to obtain therotational rate signal Ω and the force or acceleration signal Frepresenting the change in velocity, i.e. acceleration of the movingbody, along the Z axis. U.S. Pat. No. 4,510,802, commonly assigned tothe assignee of this invention, describes a control pulse generator,which generates and applies a sinusoidal signal of a frequency ω to theD'Arsonval coil to vibrate the parallelogram structure and thus thefirst and second accelerometer structures mounted thereon, with adithering motion of the same frequency ω. The accelerometer outputsignals are applied to a processing circuit, which sums theaccelerometer output signals to reinforce the linear componentsindicative of acceleration. The linear components are integrated overthe time period T of the frequency ω corresponding to the ditherfrequency to provide the force signal F, which represents the change invelocity, i.e. acceleration, along the Z axis. The accelerometer outputsignals are also summed, whereby their linear components cancel andtheir Coriolis components are reinforced to provide a signal indicativeof frame rotation. That difference signal is multiplied by a zero meanperiodic function sgnc ωt. The resulting signal is integrated over aperiod T of the frequency ω by a sample and hold circuit to provide thesignal Ω representing the rate of rotation of the frame.

The D'Arsonval coil is driven by a sinusoidal signal of the samefrequency ω which corresponded to the period T in which the linearacceleration and Coriolis component signals were integrated. Inparticular, the pulse generator applies a series of pulses at thefrequency ω to a sine wave generator, which produces the substantiallysinusoidal voltage signal to be applied to the D'Arsonval coil. A pairof pick-off coils produce a feedback signal indicative of the motionimparted to the accelerometers. That feedback signal is summed with theinput sinusoidal voltage by a summing junction, whose output is appliedto a high gain amplifier. The output of that amplifier in turn isapplied to the D'Arsonval type drive coil. The torque output of theD'Arsonval coil interacts with the dynamics of the parallelogramstructure to produce the vibrating or dither motion. In accordance withwell known servo theory, the gain of the amplifier is set high so thatthe voltage applied to the summing junction and the feedback voltage areforced to be substantially equal and the motion of the mechanism willsubstantially follow the drive voltage applied to the summing junction.

U.S. Pat. No. 4,881,408 describes the use of vibrating beam forcetransducers in accelerometers. In U.S. Pat. No. 4,372,173, the forcetransducer takes the form of a double-ended tuning fork fabricated fromcrystalline quartz. The transducer comprises a pair of side-by-sidebeams which are connected to common mounting structures at their ends.Electrodes are deposited on the beams and a drive circuit applies aperiodic voltage signal to the electrodes causing the beams to vibratetoward and away from one another, 180 degrees out of phase. In effect,the drive circuit and beams form an oscillator with the beams playingthe role of a frequency controlled crystal, i.e., the mechanicalresonance of the beams controls the oscillation frequency. The vibratingbeams are made of crystalline quartz, which has piezoelectricproperties. Application of periodic drive voltages to such beams causethem to vibrate toward and away from one another, 180 degrees out ofphase. When the beams are subjected to accelerating forces, thefrequency of the mechanical resonance of the beams changes, whichresults in a corresponding change in the frequency of the drive signal.When subjected to acceleration forces that cause the beams to be placedin tension, the resonance frequency of the beams and thus the frequencyof the drive signal increases. Conversely, if the beams are placed incompression by the acceleration forces, the resonance frequency of thebeams and the frequency of the drive signal is decreased.

Above referenced U.S. application Ser. No. 07/316,399 describesaccelerometers using vibrating force transducers require materials withlow internal damping, to achieve high Q values that result in low drivepower, low self-heating and insensitivity to electronic componentvariations. Transducer materials for high-accuracy instruments alsorequire extreme mechanical stability over extended cycles at high stresslevels. Crystalline silicon possess high Q values, and with the adventof low cost, micromachined mechanical structures fabricated fromcrystalline silicon, it is practical and desirable to create vibratingbeams from a silicon substrate. Commonly assigned U.S. Pat. No. 4,912,9describes a vibrating beam structure fabricated from crystalline siliconand including an electric circuit for applying a drive signal or currentalong a current path that extends in a first direction along a firstbeam and in a second, opposite direction along a second beam parallel tothe first. A magnetic field is generated that intersects substantiallyperpendicular the conductive path, whereby the first and second beamsare caused to vibrate towards and away from one another, 180 degrees outof phase.

Digital techniques employ stable, high frequency crystal clocks tomeasure a frequency change as an indication of acceleration forcesapplied to such vibrating beam accelerometers. To ensure preciseintegration or cosine demodulation, a crystal clock is used to setprecisely the frequency of the dither drive signal. Outputs from twoaccelerometers are fed into counters to be compared to a reference clocksignal produced by the crystal clock. A microprocessor reads thecounters and processes the data to provide a force signal F and arotational signal Ω. The main advantage of digital processing is theability to demodulate with extreme precision. The short term stabilityof the reference crystal clock allows the half cycle time basis to beprecisely equal. Thus a constant input to the cosine demodulator ischopped up into equal, positive half cycle and negative half cyclevalues, whose sum is exactly zero.

In an illustrative embodiment, the two accelerometers signals arecounted in their respective counters over a 100 Hz period (correspondingto a 100 Hz of the dither frequency ω) and are sampled at a 400 Hz datarate corresponding to each quarter cycle of the dither motion. The twoaccumulated counts are subtracted to form the force signal F. Since thecounters act as an integrator, the acceleration signal is changeddirectly to a velocity signal. Taking the difference of the accelerationsignals tends to reject all Coriolis signals as does the counterintegration and locked period data sampling.

The Coriolis signals are detected by a cosine demodulation. The cosinedemodulated signals from the first and second accelerometers are summedto produce the Δθ signal. Again, the counters integrate the rate data toproduce an angle change. The sum also eliminates any linear accelerationand the demodulation cancels any bias source including bias operatingfrequency and accelerometer bias. The accelerometer temperature is usedin a polynomial model to provide compensation for all the coefficientsused to convert the frequency counts into output units. Thus, the scalefactor, bias and misalignment of the sensor axes are corrected over theentire temperature range.

The demodulation of the frequency sample is straightforward once thedata is gathered each quarter cycle. The cosine demodulation is simplythe difference between the appropriate half cycles. The linearacceleration is the sum of all samples.

SUMMARY OF THE INVENTION

This invention employs the techniques of micromachining a substantiallyplanar substrate of a material such as silicon with a high degree ofaccuracy to produce therefrom a pair of accelerometers, whose ditheraxes, accelerometer axes and input axes are so disposed that a strenuousvibration has minimal affect upon the accelerometer output signals.

This invention provides an improved rate and acceleration sensorcomprised of a pair of accelerometers interconnected by a link so thatextraneous motion imposed on one of the accelerometers is also imposedon the other with an equal and opposite force such that any error causedby extraneous motion in the output signals of the accelerometers tend tocancel each other.

A drive mechanism imposes a dither motion to a pair of coupledaccelerometers with a simple magnetic drive circuit comprising but asingle permanent magnet and a magnetic path for directing the fluxthrough each of the accelerometers, which are both disposed in aside-by-side relation within a single plane. This magnetic circuit notonly effects dither motion, but also vibrates the accelerometer sensorin the form of a pair of vibrating beams.

In an illustrative embodiment of this invention, apparatus for measuringthe specific force and angular rotation rate of a moving body, comprisesa silicon substrate having first and second substantially planarsurfaces disposed substantially parallel to each other. A firstaccelerometer is formed of the substrate and has a first force sensingaxis for producing a first output signal indicative of the accelerationof the moving body along the first force sensing axis. A secondaccelerometer is also formed of the substrate and has a second forcesensing axis for producing a second output signal indicative of theacceleration of the moving body along the second force sensing axis. Thesubstrate is micromachined to mount the first and second accelerometerssuch that their first and second force sensing axes are both oriented atthe same angle with respect to the first and second surfaces butpointing in opposite directions, and to permit the first and secondaccelerometers to move along a vibration axis perpendicular to each ofthe first and second force sensing axes. A drive mechanism coupled toeach of the first and second accelerometers for imparting a ditheringmotion thereto of a predetermined frequency along the vibration axis.The substrate has a rate axis perpendicular to each of the first andsecond force sensing axes and the vibration axis, whereby the first andsecond output signals have a Coriolis component indicative of theCoriolis acceleration of the moving body about the rate axis.

In a further aspect of this invention, the apparatus includes a linkhaving first and second points connected respectively to the first andsecond accelerometers, a pivoting point disposed intermediate of thefirst and second connected points, and a support structure for affixedlydisposing the pivoting point with respect to the mounting structureformed of the substrate, to permit the link to pivot thereabout suchthat when one of the first and second accelerometers is moved, forimparting an equal and opposite motion to the other of the first andsecond accelerometers.

The measuring apparatus of this invention also includes a signalgenerator for producing a periodic drive signal of a predeterminedfrequency. The drive mechanism responds to the drive signal to impartinga dithering motion to the accelerometer along the vibration axis. Thedrive mechanism includes a conductive path formed on a surface of thesubstrate and is connected to the signal generator means to receive thedrive signal therethrough, and a pole piece for directing a magneticflux to cross the conductive path, whereby the interaction of themagnetic flux and the drive signal causes the accelerometer to vibratealong its vibration axis.

In a still further aspect of this invention, the drive mechanism of themeasuring apparatus imparts a dithering motion to each of the first andsecond accelerometers. A first conductive path is disposed along a firstportion of the first accelerometer, and a second conductive path isdisposed along a second portion of the second accelerometer. A unitarymagnet emanates the flux through from its first and second surfaces. Apole piece has a first surface for abutting the first surface of theunitary magnet and first and second projections having respectivelysecond and third surfaced abutting said first substantially planarsurface of the silicon substrate. These second and third projectionsurfaces are of reduced area compared to that of the first surface ofand are aligned with the portions of the first and secondaccelerometers, whereby the flux density is increased and is restrictedto flow through these portions of the first and second accelerometers.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a perspective view illustrating the rate and accelerationsensor of this invention;

FIG. 1B is a side, cross-sectional view of the sensor of FIG. 1B.

FIG. 1C is a cross-sectional, side view taken along line 1C--1C of FIG.1B.

FIG. 1D is a bottom plan view of the sensor shown in FIGS. 1A and B.

FIG. 1E is a top plan view of the flux path assembly included within thesensor as shown in FIGS. 1B, C and D.

FIG. 2A is a top plan view of the unitary substrate out of which areformed a pair of accelerometers disposed in a side-by-side relationshipwith their input axes pointing in opposite directions, as shown in FIGS.1B, 1C, and 1D.

FIG. 2B is a perspective view of one of the accelerometers formed in thesubstrate as shown in FIG. 2A.

FIG. 2C is a cross-sectional view of the substrate and its accelerometeras taken along the line 2C--2C of FIG. 2B.

FIG. 3A is a circuit diagram of a first embodiment of an oscillatorcircuit for providing drive signals to the drive coils of theaccelerometers shown in FIG. 2A.

FIG. 3B is a circuit diagram responsive to the velocity output signal ofthe circuit shown in FIG. 3A for gating the output signals from theaccelerometer into counters.

FIG. 3C is a circuit diagram of a second embodiment of an oscillatorcircuit for sensing signals derived from the pick-off coils disposed onthe accelerometers shown in FIG. 2A for providing drive signals to thecoils of these accelerometers to effect the dither motion thereof.

FIG. 3D is a functional block diagram illustrating the processing of theoutput signals from the first and second accelerometers formed withinthe silicon substrate, of FIG. 2A and, in particular, illustrates how apair of counters are gated to effectively demodulate the accelerometeroutput signals to provide an indication of the specific force andangular rotation rate of the moving body.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the drawings, FIGS. 1A, B, C and D show the arrangementof a rate and acceleration sensor 10 according to the present invention.The sensor 10 includes a shell 12 housing a unitary substrate 16, whichis illustratively made of silicon and in which is formed, illustrativelyby micromachining, a pair of accelerometers 32a and 32b disposed inside-by-side relation such that their input axes 38a and b are disposedin opposite directions (see FIG. 1D), a unitary magnet 20 and a fluxpath assembly 18, which provides a magnetic path for directing the fluxemanating from the magnet 20 through the substrate 16 and its first andsecond accelerometers 32a and b. As will be explained, the configurationand disposition of the accelerometers 32a and b within the substrate 16permits a simple, straightforward magnetic flux path to effect theoperation of the dithering motion and the vibration of a sensor elementof the accelerometers 32a and b.

Referring now to FIG. 2A, the details of the substrate 16 are shown. Thefirst and second accelerometers 32a and b are micromachined from theunitary, silicon substrate 16 so that their input axes 38a and 38b aredisposed in parallel but opposite directions. In FIG. 2A, the input axis38a of the accelerometer 32a is disposed out of the page, whereas theinput axes 38b of the accelerometer 32b is disposed into the page.Further, the input axes 38a and b are disposed perpendicular to a ditheror vibration axis 41 and to a rate axis 39. As is well known in the art,the accelerometers 32a and b will respond to linear acceleration alongtheir input axes 38a and b, respectively, and to rotation of thesubstrate 16 about its rate axis 39.

The substrate 16 includes a dither or mounting frame 30 from which eachof the accelerometers 32a and b is suspended respectively by a pair offlexures 34 and 36, which upon application of a dithering force vibratewith an "S bend" motion to translate the accelerometers 32a and b in apredominantly linear relationship with each other. As will be furtherdescribed, a periodic drive signal or current is applied via theexternal connectors 86a and b to a conductor or conductive path 92. Themagnet 20 emanates a magnetic field substantially perpendicular to thesurface of the substrate 16, whereby the accelerometers 32a and b aresubjected to a periodic dithering motion along their dither axis 41.

A link 72 is connected to the unsupported end of each accelerometer 32to insure that the dithering motion imparted to one of theaccelerometers 32a will be of the exact same frequency and in phase withthat applied to the other accelerometer 32b. Without a link 72therebetween, the accelerometers 32a and b would tend to vibrate atslightly different frequencies due to slight mass mismatch. Even ifdriven by a drive signal of common frequency, the accelerometer motionswould tend to be out of phase with each other. The link 72 is connectedby a flexure 80a to the free moving end of the first accelerometer 32aopposite to the flexures 34a and 36a, which mount the accelerometer 32ato the dither frame 30. The link 72 resembles a lever pivotally mountedabout a pivot point 73 provided by a pivot flexure 82. The link 72includes first and second lever arms 74a and b extending in oppositedirections from the pivot point 73. The second lever arm 74b isconnected by a flexure 80b to the free moving end of the accelerometer32b opposite to its end connected by the flexures 34b and 36b to thedither frame 30. The link 72 includes a pair of parallel members 76a and76b interconnecting the pivot arms 74a and 74b to a brace 78 connectedto the pivot flexure 82. In turn, the pivot flexure 82 is mounted alonga center axis of the substrate 16 by a support member 84, which is inturn affixed to the dither frame 30.

As more fully shown in FIG. 2B, each accelerometer 32 includes anelement 48 sensing the acceleration imposed on the sensor 10 andincluding a pair of vibrating beams 54 and 56, which are driven tovibrate in opposite directions as indicated by the arrows 57' and 57",respectively. It will be appreciated that the arrows 57' and 57" arealigned in a parallel relationship with the dither axis 41 and aredisposed perpendicular to the input axes 38a and b and to the rate axis39 (see FIG. 2A). One end of each of the vibrating beams 54 and 56 isaffixed in a relatively stationary relationship to an accelerometersupport frame 42. The remote ends of the vibrating beams 54 and 56 areconnected to a proof mass 40, which is suspended by a pair of hinges 44and 46 to the frame 42. As shown in FIG. 2B, the hinges 44 and 46 definea hinge axis 47 about which the proof mass 40 rotates. When acceleratingforces are applied along the input axis 38 of each accelerometer 32, itsproof mass 40 tends to pivot about its hinge axis 47. The opposite endof the proof mass 40 is pliantly or flexibly connected to theaccelerometer support frame 42 by a strut 52 of reduced cross-section,whereby the proof mass 40 is free to move along its input axis 38. Asshown in FIG. 2C, the hinges 44 and 46 are formed by micromachining thesilicon substrate 16 into a relatively thin flexure with respect to thewidth of the support frame 42, whereby the proof mass 40 is permitted topivot about the hinge axis 47.

As shown in FIGS. 2A, B and C, each of the accelerometers 32a and b hasa corresponding strut 52a or b, which tends to dampen or attenuateextraneous movements applied to the proof masses 40a or b. A pendulousaxis 53 is associated with each of accelerometers 32 and its proof mass40. As best shown in FIG. 2C, each proof mass 40 has a center of gravity50. The input axis 38 of each accelerometer 32 intersects the center ofgravity 50 and is disposed perpendicular to the pendulous axis 53. Thependulous axis 53 passes through the center of gravity 50, the hingeaxis 47 and the strut 52. In an illustrative embodiment of thisinvention, the input axis 38 is tilted at an acute angle ofapproximately 8° with respect to the unitary substrate 16 and itssupport frame 42. Also the dither axis 41 intersects the centers ofgravities 50a and b of both accelerometers 32a and b and isperpendicular to their input axes 38a and b. Undesired moments may beproduced by acceleration forces acting along the hinge axis 47 todevelop moments about the pendulous axis 53 equal to the product of suchforces times a moment arm or equivalent radius of rotation 55corresponding to the vertical distance between the rate axis 47 and thecenter of gravity 50. In a preferred embodiment, each strut 52 is madeof reduced cross sectional dimensions, e.g., 1 millinch square. A foot58 is disposed at right angles to the strut 52 to interconnect the endof the strut 52 to the proof mass 40. One end of the strut 52 isconnected to an innerperipheral edge of the accelerometer support frame42, and its foot 58 is connected to an edge of the free end of the proofmass 40 remote from its hinges 44 and 46 and its hinge axis 47. Bymaximizing the length of the strut 52, its spring rate is reduced toprovide maximum flexibility of the strut 52. The foot 58 is soconfigured and dimensioned to render it relatively flexible, so that thefoot 58 will "S-bend" to allow rotation of the proof mass 40substantially only about its hinge axis 47.

The vibrating beams 54 and 56 are also machined from the substrate 16but on a surface of the substrate 16 opposite to that of the hinges 44and 46. Thus, as acceleration forces cause the proof mass 40 to rotateupwardly as shown in FIG. 2C, both of the vibrating beams 54 are putinto compression, whereas when the proof mass 40 is pivoted downwardlyas shown in FIG. 2C, the vibrating beams 54 and 56 are placed intension. When the vibrating beams 54 and 56 are placed in tension, thefrequency of their natural vibration increases, and when put intocompression, that frequency decreases.

As shown in FIGS. 2A and B, a drive signal or current is applied viaconnector pads 62 via a conductive path or conductor 60 that extends ina first direction along the vibrating beam 54 and in a second, oppositedirection along the vibrating beam 56, whereby in the presence of amagnetic field as generated by the magnet 20, the vibrating beams 54 and56 vibrate in opposite directions. A drive circuit 64 is incorporated inthe accelerometer support frame 42 to provide the current to theconductor 60. The drive circuit 64 also provides an output to theexternal connector path 70, indicative of the frequency at which thevibrating beams 54 and 56 are vibrating.

A significant advantage of this invention resides in the placement ofthe first and second accelerometers 32a and b within the siliconsubstrate 16, whereby a single magnet 20 may be employed to directmagnetic flux through each of the accelerometers 32a and b for the dualpurposes of imparting the dithering motion to the accelerometers 32a andb, and imparting a vibrating motion to the sensor elements 48 in theform of the vibrating beams 54 and 56. FIG. 1E shows the flux pathassembly 18 in its flat state, before it is folded into theconfiguration shown in FIG. 1D. The assembly 18 supports and retains thesubstrate 16, a pole piece 22 and the magnet 20 in the positions asshown in FIGS. 1C and D, and includes a bottom member 100, opposing sidemembers 106a and 106b and top members 108a and b. In turn, the assembly18 is supported within the housing cover 12 by a pair of support legs110a and b, which extend downward to mate with a housing ring 14 and, inparticular, a projection 15, whereby the assembly 18 is securely heldwithin the assembled housing cover 12 and base 14.

As particularly shown in FIG. 1C, the assembly 18 provides a flux paththerethrough for the flux emanating from the magnet 20, and concentratedor focused by the pole piece 22 to pass primarily through the first andsecond accelerometers 32a and b, before the flux returns into therestricted legs 102a and b. Thereafter, the flux passes through the sidemembers 106a and b and their respective top members 108a and b and intothe magnet 20 to complete the flux path. The structure described, and inparticular the pole piece 22 and the restricted legs 102a and b,concentrate the flux to pass primarily through the accelerometers 32aand b, such that when drive signals are applied to pass through theconductors 92 and 60, a dither motion is imparted to the accelerometers32a and b, and a natural vibration motion is imparted to the vibratingbeams 54a and b, and 56a and b. The pole piece 22 has a pair ofprojections 118a and b of approximately the same dimensions as thecorresponding cross-sectional areas of the accelerometers 32a and b suchthat the flux passes primarily through the accelerometers 32a and b. Asshown particularly in FIGS. 1A and E, the restricted legs 102 form anopening 104 therethrough in which only a nominal flux appears, it beingunderstood that most of the flux is concentrated to pass through thelegs 102a and b. It is estimated that this configuration of the fluxpath assembly 18 doubles the strength of the flux passing through theaccelerometers 32a and b, thus increasing proportionally the voltageappearing on the pickup coils and, thus, reducing the gain of that drivecircuit 127' to be explained with respect to FIG. 3C. Thus, because ofthe placement of accelerometers 32a and b in a side-by-side relationshipwithin a single substantially planar substrate 16, a single magnet 20and a simple flux path assembly 18 may be employed to provide themagnetic flux to effect efficiently both the dithering and vibratingmotion of accelerometers 32a and b.

As shown in FIG. 2A, the conductive path 92 is deposited on the topsurface of the substrate 16 and extends from the external connector 86adown a leg of the dither frame 30, horizontally across the flexure 36aand the bottom peripheral edge of the accelerometer 32a, down thevertical flexure 80a, across the link arms 74a and 74b, down thevertical flexure 80b, across the upper peripheral edge of accelerometer32b and its flexure 34b, and down the opposing leg of the dither frame30 to the external connector 86b. The conductive path 92 has a centerpoint, which is connected by a conductive path 92c and a ground terminal88 to ground. In order to maximize the efficiency of generating thedither motion, the conductive path 92 follows a path along the bottomportion of accelerometer 32a and its flexure 36a and the upper portionof the accelerometer 32b and its flexure 34b, which portions are closestto the center of the substrate 16, whereby the magnetic flux emanatingfrom the magnet 20 and focussed by the pole piece 22 and its projections118a and b, is concentrated to pass through these portions of theconductive path 92. The conductive path 92 includes a first effectiveportion identified by the numeral 92a mounted on the flexure 36a and thebottom of the accelerometer frame 42a of the accelerometer 32a and asecond effective portion 92b similarly but oppositely mounted on theaccelerometer 32b, both effective portions 92a and b disposed within theconcentrated magnetic flux produced by the magnet 20 and its pole piece22. By so configuring the conductive path 92 and its effective portions92a and b, the driving force of the dither motion is maximized.

As shown in FIG. 1A, the substrate 16 is provided with a pair of dustcovers 17a and b disposed respectively upon the opposing surfaces of thesubstrate 16. The dust covers 17a and b may also be made of silicon andserve to protect the accelerometers 32a and b from dust. Illustratively,the inner surfaces of the dust covers 17a and b are recessed (not shownin the drawings) to permit movement of the proof masses 40a and b and toprovide stops for them.

As described above, the input axis 38 is oriented at an acute angle withrespect to a line perpendicular to the surface of the substrate 16. Inan illustrative embodiment of this invention, the assembly 18 mounts thesubstrate 16 at a compensating angle with respect to the axis of thehousing shell 12, whereby the sensor 10 and thus, the input axes 38 ofthe accelerometers 32a and b may be precisely oriented with respect tothe vehicle or aircraft carrying the sensor 10 of this invention. Thesubstrate 16 is mounted on a plurality of pads 114. A pair of supportarms 112a and b extend from the leg 102a to support the corners of thelower surface (as seen in FIG. 1E) of the substrate 16. In turn, asupport arm 116 connects the pad 114c to the leg 102b of the assembly18, whereby the pad 114c supports a center portion of the opposite edgeof the substrate 16. The numeral 113 designates the center of theopening 104 and is aligned with the pivot point 73, when the substrate16 is mounted within the flux path assembly 18 as shown in FIG. 1A. Thepivot point 73 forms the center of the silicon substrate 16 as shown inFIG. 2A. Similarly, the axis of the permanent magnet 20, shown in FIG.1B as being of a cylindrical configuration, is also aligned with thecenter 113 and the pivot point 73.

The assembly 18 solves a thermal stress problem resulting from thedifferent coefficients of thermal expansion of the silicon substrate 16and the flux path assembly 18, i.e., the assembly 18 expands at agreater rate than the silicon substrate 16. Illustratively, the siliconsubstrate 16 has a temperature coefficient of expansion in the order of2.5 PPM/° C., whereas the assembly 18 is made of a silicon steel (havinga silicon content of 3%), which in turn exhibits a temperaturecoefficient of in the order of 11 PPM/° C., which is considerablygreater than that of the substrate 16. In the absence of thermal stressrelief, the substrate 16 would tend to buckle, possibly break and/orseparate from the assembly 18. If the substrate 16 warps, the criticalalignment of the accelerometers 32a and b and its various parts will bethrown out of balance with the result that the desired compensation ofextraneous motions applied to the sensor 10 will be defeated. As shownin FIG. 1E, each of the support arms 112a and b, and 116 is disposedperpendicular respectively to each of a corresponding plurality ofradial stress lines 111a, b and c. Thus, as the assembly 16 expands andtends to place a radial stress on the arms 112a, b, and 116, theirconfiguration as shown in FIG. 1E permits them to readily flex under thethermal stress rather than buckle or break the substrate 16. Inaddition, each of the mounting pads 114a, b, and c is connected to thesubstrate 16 by a resilient adhesive such as an epoxy.

As the temperature of the permanent magnet 20, the assembly 18 and thesubstrate 16 vary, the mounting structure provided by the assembly 18and the relative positions of the permanent magnet 20 and the substrate16 therewith ensure that as the substrate 16 and it's assembly 18 expandat different rates, the relative positions of these elements withrespect to the magnet 20 remain the same. Therefore, the accelerometers32a and b remain in the same relative relationship with the permanentmagnet 20 and are exposed to a magnetic flux field of the same strength.If the magnet 20, the assembly 18 and the substrate 16 were mounted suchthat the magnet 20 could shift even to a small degree with respect tothe accelerometers 32a and b, the flux emanating through the effectiveportions 92a and b and the conductive paths 60 associated with vibratingbeams 54 and 56 would also vary, whereby any extraneous motion impartedto the accelerometers 32a and b, as well as the outputs derived from theconductors 60 of each of the accelerometers 32a and b, would differ fromeach other.

The arrangement as shown in FIG. 2A of the accelerometers 32a and b,their supporting flexures 34 and 36 and the interconnection therebetweenby the link 72 provide equal and opposite dither motion to theaccelerometers 32a and b, and isolate the substrate 16, its dither frame30 and the accelerometers 32a and b from extraneous stress, such thaterror signals are not introduced by data processing into the resultantforce signals F and rotational signals Ω and permits data processingusing the output of the accelerometers 32a and 32b by relatively simpledifferentiating and scaling techniques. Further, the structure of FIG.2A may be implemented by micromachining techniques upon a siliconsubstrate 16, whereby the resultant structure is produced at a low costand with a precision of which the prior art accelerometers were simplynot capable. In turn, the extreme accuracy of construction afforded bymicromachining techniques permits the relative placement ofaccelerometers 32a and b and its link 72 to a precision in the order of40 micro inches. As a result of such accuracy, the accelerometers 32aand b are placed in precise balance with each other such that extraneousmovements imposed upon the frame 30 do not upset this balance andintroduce erroneous signals into the outputs of the accelerometers 32aand b as may be otherwise caused by even slight misalignment of theaccelerometers 32a and 32b.

First, the accelerometers 32a and 32b are mounted upon opposing sides ofthe dither frame 30 by their flexures 34a and 36a and 34b and 36b,respectively. Each of the flexures 34 and 36 is formed from the siliconsubstrate 16 to a height equal to the width of the substrate 16,illustratively of 20 mils, and a thickness of 1.4 mil corresponding tothe vertical dimension of the flexures 34 and 36 as shown in FIG. 2A.The length of each of the flexures 34a and b and 36a and b is selectedto provide a spring rate relative to the mass of accelerometers, e.g.,of 0.1 gram, that will cause the flexures 34 and 36 to flex in an"S-bend" when subjected to the dither motion. The spring rate of theflexures is proportional to T³ /L³, where T is the thickness of theflexures 34 and 36 and L is the length thereof. The length L andthickness T of the flexures 34 and 36 are set such that when dithermotion is applied, the flexures 34 and 36 then flex in an Sconfiguration, as shown in FIG. 2A. Such "S-bend" flexures 34 and 36permit the accelerometers 32a and b to translate with predominantlylinear motion, i.e., the vibrating beams 48a and 48b (as well as theother elements) of accelerometers 32a and 32b remain substantiallyparallel to each other as they are dithered along the dither axis 41. Inaddition, the flexures 34 and 36 permit accelerometers 32a and 32b tomove in a predominantly linear fashion with only an insignificantnonlinear frequency component imposed thereon.

The link 72 mechanically interconnects the first and secondaccelerometers 32a and b so that any motion include dithering motion andextraneous motions applied to one of the accelerometers 32, will also beapplied in precisely equal and opposite fashion to the otheraccelerometer 32. In this fashion, the outputs of the accelerometers 32aand b may be processed simply by sum and difference techniques toprovide a force signal F and the rotational signal Ω, as well as tocancel out erroneous signals. Without the link 72, the accelerometers32a and 32b would operate at different frequencies due to slight massmismatch of the proof masses 40. If driven at a common frequency, theaccelerometers 32a and 32b would without the link 72 operate out ofphase with each other (other than 180°).

The configuration and the manner of mounting the link 72 are effected topermit the link 72 to effectively pivot about the pivot point 73intersecting an axis passing through the lever arms 74a and b. The pivotpoint 73 is disposed at a selected point along the length of the pivotflexure 82. As shown in FIG. 2A, the bottom end of the pivot flexure 82is affixed to the support member 84 and extends vertically along thedither axis 41. The length of the pivot flexure 82 is selected, e.g.,100 mils, to impart a simple bending thereto, whereby that portion fromthe pivot point 73 to the point of interconnection to the link 72 ispermitted to flex about the pivot point 73, while the remaining portionof the flexure 82 between the pivot point 73 and the support member 84,flexes in a smooth arc. In this fashion, the end points of the link 72are disposed a radial distance from the pivot point 73 equal to theeffective radius of rotation provided by the "S-bend" flexures 34 and 36for the accelerometers 32a and 32b.

As indicated above, the length of the pivot flexure 82 is determined sothat it flexes with only a simple arc bending. To accommodate a pivotflexure 82 of the desired length, it is necessary to configure the link72 with a U-shaped configuration comprised of the parallel members 76aand b and the interconnecting member 78. In addition, a portion of thesupport member 84 is removed to provide a cut out 85, whereby the lengthof the pivot flexure 82 is set to provide the simple bend motion.

The vertically oriented flexures 80a and b as shown in FIG. 2A aredimensioned and, in particular, their lengths are set such that theyexhibit 50% simple arc bending and 50% "S-bend" motion. Opposite ends ofthe vertical struts 80a and b are respectively interconnected between anedge of one of the accelerometers 32a and b and an end of one of thelink member 4a and b. Portions of the link 72 and the accelerometers 32are removed to provide cutouts 71 and 39, respectively, so that theprecise length of the flexures 80a and b is determined to ensure thatthe flexures 80 have characteristics of 50 percent simple motion and 50percent "S-bend" motion. Further with such characteristics, it isassured that any motion imparted by the flexures 80 to one of theaccelerometers 32 is imparted as a sinusoidal function to the otherwithout introducing a higher order harmonic into the translation motion.Without such flexures 80 and the link 70, the dither motion as well asother extraneous motion applied to the subscript 16, could impose highorder harmonic motion to the accelerometers 32a and b, whose outputsupon demodulation would bear an undesired bias signal.

As indicated above, the flexures 34 and 36 are made of such dimensionsand, in particular, their length such that they flex with an "S-bend".In particular, one end of each of the flexures 34 and 36 is respectivelyaffixed to the inner periphery of the dither frame 30 and the other endto the accelerometer 32. An external edge portion of the accelerometersupport frame 42 is removed to provide a cut out 33 so that the lengthof the flexures 34 and 36 is critically set to provide the desired"S-bend" motion and so that the other end of the flexures 34 and 36 areconnected to a midpoint of the horizontal edges of accelerometers 32aand b. As shown in FIG. 2A, the flexures 34 and 36 supportaccelerometers 32a and b so that their centers of gravity 50 and thepivot point 73 lie along the central axis of the substrate 16 so thatthe center axis coincides with the dither axis of 41.

The "S-bend" flexures 34 and 36 have respectively pivot points 35 and37, which are disposed a distance 1/6th of the flexure length from theinner periphery of the dither frame 30. The "S-bend" flexures 34 and 36form respectively an effective radius from their pivot points 35 and 39to their points of connection with their support frames 42. Thateffective radius equals to 5/6 of the length of the flexures 34 and 36,which in turn precisely equals the radius provided by the lever arms 74from their pivot point 73 to the points of interconnection of theupright flexures 80a and b to the extremities of the lever arms 74a andb. By providing the link 72 and the accelerometers 32a and b with equalradii of rotation about the respective pivot points 73, and 37 and 35,it is assured that the link 72 will provide equal and opposite motion tothe accelerometers 32a and b. As a result, if any extraneous noise isapplied to one of the accelerometers 32a and b, a like and oppositemotion will be applied to the other, so that upon processing any noisein the outputs of the accelerometers 32 is effectively removed by sumand difference techniques.

Upon application of the dithering motion to the accelerometers 32a andb, the "S-bend" flexures 34 and 36 move up and down in a substantiallyparallel relationship to each other due to the "S-bend" flexing of theirflexures 34 and 36. Each flexure 34 and 36 has a center point 39 and 40,respectively. The bending motion resembles two smooth curves, the firstterminating at the center point in one direction and the second curvewith an opposite curve meeting the first at the center point. The"S-bend" flexures ensure that the horizontal and vertical edges of thesupport frames 42a and b remain precisely parallel with the innerhorizontal and vertical peripheral edges of the dither frame 30.

As indicated above, the "S-bend" flexures 34 and 36 provide an effectiverotation of the accelerometers 32a and b about their pivot points 35 and37. In an illustrative embodiment, the commonly applied dithering forcesmove accelerometers 32a and b through a positive and negative angularrotation with respect to their rest positions, whereby the center ofgravities 50a and b move from the center axis of the substrate 16 adistance of only 37 microinches for a dithering motion having anamplitude of 1 mil along the dithering axis 41.

The construction of accelerometers 32a and b from the silicon substrate16 results in extremely close alignment of the accelerometers 32. Thisresults from the high degree of flatness of the silicon substrate 16 andthe relative proximity of the accelerometers 32a and b micromachinedfrom the substrate 16. The flexures 34, 36, 80 and 82 are produced byetching near the surfaces of the substrate 16. Such micromachiningensures that the input axes 38a and b will be precisely perpendicular tothe dither axis 41, at least as good as the flatness and parallelrelationship of the surfaces of the silicon substrate 16, which cantypically be achieved to a high degree. Thus, this invention achievesclose alignment of the input and dither axes 38 and 41, thus overcomingthe problem of prior art Coriolis sensors with regard to such alignment.The suspension of the accelerometers 32a and b by their flexures 34a and36a, and 34b and 36b from opposing sides of the dither frame 30 so thattheir input axes 38 a and b point in opposite directions and the use ofthe link 72 provide excellent nonlinearity motion cancellation.

The well known Euler-Buckling curves represent the structural tensioningand compression characteristics of the accelerometers their vibratingbeams 54 and 56. The back-to-back orientation ensures that when thevibrating beams 54 and 56 of the accelerometer 32a are in tension, thebeams of the other accelerometer 32b are in compression, and vice versa.As will be explained, the outputs of the accelerometers 32a and 32b aresummed together to provide an indication of linear acceleration. Thisorientation insures that the beams 54 and 56 are operating incomplementary portions of these curves and the summed outputs of theaccelerometers 32a and b provide an accurate indication of the linearacceleration by canceling the higher order nonlinearities of thevibrating beams 54 and 56. In addition, extraneous movements acting onthe accelerometers 32a and b will at least to a first order of measure,tend cancel or dampen each other, whereby extraneous signals do notappear in the summed accelerometer outputs. In an analogous fashion whenthe difference of the accelerometer outputs is taken, the cancelingcharacteristics of these curves ensure that second order nonlinearitiesin the resultant angular rotation signal will also average.

The construction of the two accelerometers 32a and b from the siliconsubstrate 16 offers other advantages. First, the configuration and thedimensions of the accelerometers 32, the various flexures and the link72 may be determined with an extreme degree of accuracy, e.g., 40microinches, so that the relative position of these elements iscontrolled to a like degree. Second, the construction of the flexures inthe plane of the silicon substrate 16 ensures that the accelerometers 32are dithered in that plane. As noted above, the link 72 ensures that theaccelerometers 32a and b move in equal and opposite directions under theinfluence of the applied dithering motion. Thus, the centers 50a and bof gravity of the accelerometers 32a and b are placed precisely upon thecenter axis of the substrate 16, which is aligned with the dither axis41 with a high degree of precision, whereby the dither motion caused bythe current passing through the drive coils a and b causes the ditheringmotion to be applied precisely along the center axis of the substrate16. Such accuracy ensures that extraneous motions otherwise resultingfrom the dither motion are not imposed upon the accelerometers 32a andb.

Secondly, the suspension of accelerometers 32a and b by the "S-bend"flexures 34 and 36, which are also formed in the plane of the siliconsubstrate 16, produces a motion of the accelerometers 32a and b ofrelatively small, opposing arcs as a result of this dithering motion. Inone illustrative embodiment, dithering at maximum displacement(amplitude) of 1 millinch (corresponding to 1 degree of the total peakto peak angular travel), displaces the accelerometers 32a and b fromtheir center axis by a mere 37 microinches. During a single cycle ofmotion of each of the accelerometers 32a and b up and down along thedither axis 41, each accelerometer 32 is subjected to 2 translations asit rotates about its effective radius provided by its flexures 34 and36. However, since these double translations or "bobbings" occur withinthe plane of the silicon substrate 16 and not along the input axes 38aand b, the problems that have occurred with the prior art sensors ofparallelogram configuration are avoided. First, a corresponding doublefrequency error signal is not imposed upon the inputs of theaccelerometers 32, which required a phase servo adjustment in theprocessing as described in U.S. Pat. No. 4,799,385. Second, there is noneed to offset the center of oscillation or to couple turn-aroundacceleration into the accelerometer input axis. As a result, for anyposition of the accelerometers 32a and b during their dithering motion,there is very little double frequency motion imposed upon their inputaxis 50. Thus, there is no need to "steer" out the misalignment byadding a bias to the dither drive signal.

The various features of the silicon substrate 16 may be micromachined byvarious techniques well known in the prior art such as a wet chemicaletch or a dry chemical etch such as plasma etching, sputter etching orreactive ion etching. For a detailed discussion of such techniques,reference is made to the following publications, which are incorporatedherein by reference: VLSI Fabrication Principles by Sorab K. Ghandhi andSilicon Processing for the VLSI Era, Vol. 1 - Process Technology by S.Wolf & R. J. Tauber.

In this illustrative embodiment of the silicon substrate 16, the maximummisalignment of the accelerometers 32 from the substrate center axiswould be less than 0.1 mrad. This has the benefit of not fully imposingsecond harmonic distortion resulting from the dither drive into therotational component signal outputted by the accelerometers 32a and b.Otherwise, as is disclosed by the prior art parallelogram drivearrangements, such second harmonic drive distortion could be multipliedby the squaring action of double dipping to generate primary and thirdharmonics, which can be coupled into the rate channels as error. Theseerrors are avoided by the side-by-side placement and accuratemicromachining of the accelerometers 32a and b within the substrate 16.

As noted above, each of the accelerometers 32a and b is suspended by"S-bend" flexures 34 and 36, which provide effective radii of rotationequal to that radius provided by the link arms 74a and b; without suchconstruction, the accelerometers 32a and b would dither with anon-sinusoidal motion, which would introduce high order harmonicdistortion in the rate signal. It is contemplated that there will besome coupling due to the offset of the input axis 50 resulting from thecenters 50 of gravity being disposed above the flexures; however, suchcoupling is minor compared to that introduced by the parallelogramstructures of the prior art.

Referring now to FIG. 3A, there is shown a dither drive circuit 127 forproviding a sinusoidal voltage to be applied across the effectiveportions 92a and b. The conductive path 92 forms the first effectiveportion 92a for imparting a vibrating motion to the accelerometer 34aand the second effective portion 92b for imparting a vibrating motion tothe accelerometer 32b. The center point of the conductor 92 is connectedto ground via the conductor 92c and a ground terminal 88. As shown inFIGS. 1A and 1D, a magnetic field is generated perpendicular to thesurfaces of the substrate 16 and is focused by the pole piece 22 throughthe accelerometers 34a and 34b. Illustratively, the conductor 92 takesthe form of a deposit of gold. In an illustrative embodiment of thisinvention wherein the length of the conductor 92 extending betweenterminals 86a and 88 (or 86b and 88) is approximately 1 inch and isdeposited to a depth of 1μ meter and a width of 10μ meter, theresistance offered by such a length of the conductor 92 is in the orderof 100 ohms. When the magnetic flux crosses the conductive path 92, avoltage is induced thereacross of approximately 0.5 volt, which isapproximately 2500 times the voltage amplitude of the velocity signalwhich is outputted by the dither drive circuit 127 of FIG. 3A on itsoutput 86-91. To effectively remove this resistance voltage, a bridge125 shown in FIG. 3A is employed with one leg thereof being formed bythe effective portions 92a and b connected in parallel, and a second legby a reference conductor 93 which is disposed on the dither frame 30 andhas ends connected to terminals 91 and 95, as shown in FIG. 2A. Theeffective portions 92a and b are connected in parallel by connecting theterminals 86a and b together; in turn, the terminal 88 forms one node ofthe bridge 125 and the connected terminals 86a and b another node. Theconductive path 92 forms the two effective portions 92 a and bconnected, with the interconnecting portion of conductor 92 beingconnected via the conductive path 92c to the ground terminal 88. Theeffective portions 92a and 92b are connected in parallel to form one legof the bridge 125. The other leg of the bridge 125 is formed of thereference conductor 93 having one-half the length of the conductor 92between the terminals 86a and 88 (or 86b and 88), e.g., one-half inch.The reference conductor 93 is made of the same material as that ofconductor 92, e.g., gold, and is deposited to a like depth, whereby alike voltage, e.g., 0.5 v, is developed across both of the parallelconnected effective portions 92a and b, and the reference conductor 93.A single drive voltage is applied from a first bridge node 129 toground, whereas an output of the bridge 125 as developed across bridgenodes 86 and 91 is taken and applied to a first operational amplifier128, which subtracts the voltage developed across the referenceconductor 93 from that developed across the parallel connected effectiveportions 92a and b . A second operational amplifier 130 provides theremaining gain to boost the output of the first operational amplifier128 to approximately 2.5 v peak at the output 132. A feedback path isconnected to the bridge circuit 125 providing position feedback plus anexcess phase shift due to the high-order operational amplifier poles,whereby an oscillating circuit is established to provide the sinusoidalsignal to drive the effective portions 92a and b. The output 132 isclamped by a pair of Zener diodes D1 and D2 connected in oppositionbetween the output 132 and ground, to clamp the output 132 and therebystabilize the drive signal applied to the effective portions 92a and b.

As shown in FIG. 3B, the velocity signal appearing on the output 132 ofthe dither drive circuit 127 is applied to a zero-crossing detectorcircuit 133, whose outputs are used to gate the counters for countingthe crystal clock signal, whereby the Coriolis rate signal andacceleration force signal can be demodulated. The velocity signal iscoupled to an operation amplifier 134 by a capacitor C1 and resistor R10to generate a zero-crossing signal. The open loop gain of theoperational amplifier 134 "squares" the velocity signal and applies the"squared" signal to a pair of CMOS logic gates 136 and 138 connected inparallel with each other; these gates effect a voltage shift of thesignal to levels compatible with the counters, e.g., 0 to + or -5 v.Another inverting logic gate 140 inverts the signal. The signalsillustrated in FIG. 3B are applied to the counters 152 and 154, as shownin FIG.3D, to count a signal indicative of the resonant, naturalfrequency for each half cycle of the dithering frequency f, whereby theCoriolis rate component is demodulated by inverting every other sample.As described in detail in U.S. Pat. No. 4,590,801, the acceleration isthe sum of each such sample.

Referring now to FIG. 3C, there is shown an alternative of embodiment ofthe dither drive circuit 127', which provides a dither drive signalacross the external connectors 86a and 86b to the effective portions 92aand b. As described above, a magnetic field is generated and directed bythe magnet 20 and its flux path assembly 18 perpendicular to thesurfaces of the substrate 16 and the effective portions 92a and bdisposed thereon, whereby a force is generated by the current flowingthrough the effective portions 92a and b to move the accelerometers 32aand b in a substantially rectilinear, vibrating movement up and downalong the dither axes 41 as shown in FIG. 2A. The accelerometers 32a andb vibrate or dither at the frequency f determined by the mechanicalcharacteristic including the spring rates of the flexures 34, 36, 80 and82 the mass of the accelerometers 32a and b. The dither drive signaloutputted by the dither drive circuit 127' is of a frequencycorresponding to the frequency f of dither vibration and, as explainedabove, is used in the further processing of the accelerometer outputs todemodulate those signals to provide a force signal F and a rotationalsignal Ω. Further, a wire (not shown) is disposed on the opposite sideof the substrate 16 (from that shown in FIG. 2A) and forms first andsecond pick-off portions 92a' and 92b'. The innerconnection of thepick-off portions 92a' and 92b' deposited on the opposite side to groundis more clearly shown in FIG. 3C. As accelerometers 32a and b arevibrated, the pick-off portions 92a' and b' move through the magneticfield created by the unitary magnet 20 and its assembly 18, a current isinduced therein and the resultant voltage is applied via resistors R11and R12 to a pair of operational amplifiers 142 and 144 to besuccessively amplified with a relatively high gain, before being appliedas the dither drive signal to the effective portions 92a and b. Zenerdiodes D4 and D5 serve to clamp the dither drive voltage as derived fromthe output of the operational amplifier 144 to a known voltage level.

The configuration of the accelerometers 32a and b within their siliconsubstrate 16 and the flux path assembly 16 and its unitary magnet 20develop a considerable force in excess of that minimum turn-aroundacceleration required to effect the dither motions of accelerometers 32aand b. It is understood in the art that a minimum turn-aroundacceleration is needed to cause each of the accelerometers 32a and b tostop going in one direction and to accelerate in the opposite, wherebythe dithering motion may occur. The acceleration force F tending tocause the dithering motion of accelerometers 32a and b is set out by thefollowing equation:

    F=mg=l·i×B,                                 (1)

where i is the current passing through the conductive path 92 making upthe effective portions 92a and b, l is the effective length of thatportion of the conductive path 92 within the magnetic flux passingthrough the accelerometers 32a and b, i.e., the length of the effectivepositions 92a and b, and B is the magnitude of the flux. In anillustrative embodiment of this invention, a current of 5 milliamp maybe applied to each of the effective portions 92a and b, the effectiveportions 92a and b may have an effective length l of 6 mm and 8kilogauss may be readily provided by the magnet 20 and its assembly 18.Solving equation (1) for mass m, where g is the universal gravityconstant, it is shown that a force of 2.4 milligrams may be readilydeveloped by this illustrative embodiment. In such an embodiment, theresonant frequency of the dithering motion imposed upon theaccelerometers 32a and b is approximately 500 hz and a displacement D ofaccelerometers of 1 millinch. The drive acceleration a may be calculatedby the following: ##EQU1## where D is the displacement, f is the ditherfrequency and K is a conversion factor. The calculated force for 1millinch of displacement D at 500 Hz is 25 g's peak acceleration. Wherethe mechanical gain of the spring mass system formed by accelerometers Qis set at a modest value of 1,000, the force developed by theinteraction of a current passing through the conductive path 92 and themagnetic flux directed through the accelerometers 32, is 0.025 g's (25g's/1,000). This force is sufficient to accelerate the calculated massforce of 0.024 grams. It is noted that the Q of pure crystals may be ashigh as 10,000, demonstrating that the dithering system described aboveis more than capable of developing sufficient force to effect therequired dithering drive motion.

The following calculations demonstrate that the values of ε, the voltageinduced in the pick-off portions 92a' and 92b', is relatively highcompared to the noise found in those operational amplifiers as would beincorporated into the drive circuit 127', as shown in FIG. 3C. Values ofε are provided by the following equation:

    ε=v×B·l,                            (3)

where v is the amplitude of the velocity output signal of theaccelerometers 32, B is the strength of the magnetic field crossing theeffective portions 92a and b, l is the effective length of the conductorwithin the magnetic flux field. For a dither displacement D of 1milliinch, a natural frequency of accelerometer of 500 Hz, a velocitysignal v of approximately 8 cm/sec., a length l of the effectiveportions 92a and b of 6 mm, and a flux strength of 8 kilogauss, theoutput of a single pick-off portion 92a' is 0.4 mv. If the outputs ofaccelerometers 32a and b are connected in series, the output voltage isdoubled to 0.8 mv. An operational amplifier, as may be incorporated intothe drive circuits of FIGS. 3A and C, typically has a noise of 0.1 μvfor a bandwidth of 10 K Hz. If the operational amplifier has a gain of3×10³, its output may typically be 2.4 v peak, providing a noise to peaksignal ratio of 0.01%, which is a good indicator that the sensor 10 ofthis invention is a good velocity sensor for the inherent of noise levelfound in the available operational amplifiers.

The accuracy with which the rate and acceleration sensor 10 may be made,the symmetry of the accelerometers 32a and b and their suspension by theflexures 34 and 36, and the interconnection of the link 72 to imposeequal and opposite motions on the accelerometers 32a and b, have anaccumulative effect to a greatly simplify the processing of theaccelerometer output signals, essentially reducing it to a cosinedemodulation step. This can be done every half cycle, since neither sinenor double frequency sine demodulation is needed as was the case withthe parallelogram structures of the prior art. Basically, the outputs ofaccelerometers 32a and b are subtracted from each other to provide thelinear acceleration signal and to average both signals while invertingevery other sample to demodulate for the cosines to produce a rate ofrotation signal ω. Neither an alignment servo nor a phase servo isneeded for such processing thus increasing the band width of therotational acceleration signal Ω to be 1 K Hz in one illustrativeembodiment of this invention.

The rate and acceleration sensor 10 has a sensitivity to rotationalacceleration imposed about its rate axis 39, i.e. the moment of each ofaccelerometers 32a and b about the rate axis 39, which accelerationsensitivity will introduce an undesired noise component in thesubsequent demodulation processing of the accelerometer output signals.That noise component can be effectively eliminated by differentiatingthe rotation rate signal ω and scaling it. In effect, as indicatedabove, the demodulated outputs of accelerometers 32 are a measure of itsrotation rate signal ω, which can be differentiated to obtain anindication of the angular acceleration of each accelerometer 32. Sincethe dimensions and, in particular, the distance between the rate axis 39and each of the centers 50a and b of gravity is known to a high degreeof precision, e.g., 40 microinches, that equivalent radius of rotationis multiplied by a measured angular acceleration force to obtain anaccurate indication thereof of the linear acceleration caused by theangular acceleration. The calculated acceleration moment is subtractedfrom the accelerometer outputs to reduce or substantially eliminate suchacceleration sensitivity.

Referring now to FIG. 3D, there is shown how the output signals f1 andf2 as derived from the respective drive circuits 127a and c areprocessed and, in particular, are applied respectively to counters 152and 154. As explained above, as the vibrating beams 54 and 56 are placedin tension or in compression due to accelerations being applied alongthe force sensing axes 38 of the respective accelerometers 32, thefrequencies of the output signals f1 and f2 change. The dither drivecircuit 127b may preferably take the form of that circuit shown in FIG.3C or alternatively FIG. 3A. The drive circuits or signal generators127a and c may illustratively take the form of that circuit shown inFIG. 3A.

The dither drive circuit 127b provides an output signal, which isapplied to the gating circuit 133 as discussed above with regard to FIG.3B. The output of the gating circuit 133 is a pair of squared gatingsignals which are applied to the counters 152 and 154. This pair ofgating signals occur at the velocity zero-crossings to gate the counters152 and 154. This is approximately a reading at 1 k Hz or both edges ofthe velocity zero-crossings. The counters 152 and 154 count thefrequencies of the accelerometer output signals f1 and f2 with respectto a reference clock signal generated and applied by a reference clock150 to each of the counters 152 and 154. In turn, a microprocessor readsthe output of the counters 152 and 154 at an illustrative frequency of 1k Hz and process these counts to provide an indication of Δv and Δθ.

As explained in detail in commonly assigned U.S. Pat. No. 4,786,861, Δvis provided by the following equation:

    Δv.sub.i =A[(N1.sub.i -N2.sub.i)+FT+B(N1.sub.i +N2.sub.i)](4)

where v_(i) is the "ith" sample of the velocity signal, A and F arescale factors, N1_(i) is the count derived from the counter 152 over a 1k Hz (1 m sec) period for the "ith" sample, N2_(i) is the count obtainedfrom the counter 154 for the "ith" sample, T is the time period and B isthe bias correction term. As well known in the art, Δθ_(i) is providedby the following equation:

    Δθ.sub.i =a(cos N1.sub.i +cos N2.sub.i)+b(cos N1.sub.i -cos N2.sub.i)                                                 (5)

where a is a scale factor and b is a bias/correction term, and

    cos (N1.sub.i)=N1.sub.i -N1.sub.(i-1), over each 500 Hz period or (6)

    cos (N1.sub.i)=(-1).sup.i N1.sub.i, at 1 k Hz rate.        (7)

Angular acceleration α is equal to the linear acceleration as derivedfrom the output of either of the accelerometers 32a or b, divided by theequivalent radius of rotation, r_(eq) in accordance with the followingequation: ##EQU2## In turn, angular acceleration α is a function of themeasured rotation rate ω in accordance with the following equation:##EQU3## In turn, the rotation rate may be expressed as follows:##EQU4## Since the derivative of the rotation rate ω is equal toacceleration α, acceleration may be expressed by the following equation:##EQU5## Thus, correction for linear acceleration A_(linear) is providedby the following equation: ##EQU6## In turn, the microprocessor 156 isprogrammed in a conventional fashion to subtract values of A_(linear)correction from the accelerometer outputs f1 and f2 to correct forangular acceleration.

While the invention has been shown and described in detail, it isobvious that this invention is not to be considered as being limited tothe exact form disclosed, and that changes in detail and constructionmay be made therein within the scope of the invention, without departingfrom the spirit thereof.

What is claimed is:
 1. Apparatus for measuring the specific force andangular rotation rate of a moving body, comprising:a) a monolithicsubstrate having first and second substantially planar surfaces disposedsubstantially parallel to each other; b) a first accelerometer formed ofsaid substrate and having a first force sensing axis for producing afirst output signal indicative of the acceleration of the moving bodyalong said first force sensing axis, said first accelerometer having aproof mass, a support frame, and at least one flexure connecting saidproof mass to said support frame; c) a second accelerometer formed ofsaid substrate and having a second force sensing axis for producing asecond output signal indicative of the acceleration of the moving bodyalong said second force sensing axis, said second accelerometer having aproof mass, a support frame, and at least one flexure connecting saidproof mass to said support frame; d) a dither frame formed of saidsubstrate, said dither frame being of a rectangular configuration havingfirst and third opposing members and second and fourth opposing members;e) a first pair of S-bend flexures connected between said support frameof said first accelerometer and said dither frame, and a second pair ofS-bend flexures connected between said support frame of said secondaccelerometer and said dither frame, said S-bend flexures being formedof said substrate for mounting said first and second accelerometers suchthat said first and second force sensing axes are both oriented at thesame angle with respect to said first and second surfaces and such thatsaid first and second accelerometers can be moved along a vibration axisperpendicular to each of said first and second sensing axes; f) linkmeans having first and second points connected respectively to saidfirst and second accelerometers, a pivoting point disposed intermediatebetween said first and second connected points, and support means foraffixedly disposing said pivot point with respect to said frame topermit said link means to pivot there about and, when one of said firstand second accelerometers is moved, to impart an equal and oppositemotion to said other of said first and second accelerometers; g) drivemeans coupled to each of said first and second accelerometers forimparting a dithering motion thereto of a predetermined frequency alongsaid vibration axis; and h) said substrate having a rate axisperpendicular to each of said first and second force sensing axes andsaid vibration axis, whereby said first and second output signals have aCoriolis component indicative of the angular rotation of he moving bodyabout said axis.
 2. The measuring apparatus as claimed in claim 1,wherein said support means comprises a pivot flexure comprising saidpivot point.
 3. The measuring apparatus as claimed in claim 2, whereinsaid pivot flexure has a length and cross-sectional dimensions such thatsaid flexure flexes with a simple bend.
 4. The measuring apparatus asclaimed in claim 3, wherein said link means comprises first and secondarms and a U-shaped member disposed there between and interconnectingsaid first and second arms, said pivot flexure having a distal endconnected to said U-shaped member, whereby said pivot point is alignedwith said first and second arms extending therefrom in radial fashion.5. The measuring apparatus as claimed in claim 1, wherein there isincluded first and second connecting flexures for respectivelyconnecting said first and second points of said link means to said firstand second accelerometers.
 6. The measuring apparatus as claimed inclaim 5, wherein each of said first and second connecting flexures havea length and cross-sectional dimensions selected such that each of saidfirst and second connecting flexures flex with approximately 50% simpleand 50% "S-bend" movements.
 7. The measuring apparatus as claimed inclaim 5, wherein said first and second connecting flexures are connectedrespectively to that end of each of said first and second accelerometeropposite from said first and second flexure means.
 8. The measuringapparatus as claimed in claim 1, wherein a conductive path is disposedon one of said first and second surfaces to traverse said first andsecond accelerometers.
 9. The measuring apparatus as claimed in claim 8,wherein said conductive path extends across one flexure of each of saidfirst and second pairs and across said link means.
 10. The measuringapparatus as claimed in claim 9, wherein there is included signalgenerator means for producing and applying a periodic drive signalhaving a predetermined frequency to said conductive path, and magneticflux producing means for producing and directing a magnetic flux tocross said conductive path, whereby the interaction of said magneticflux and said drive signal passing through said conductive path causesaid first and second accelerometers to vibrate along said vibrationaxis at said pre-determined frequency.
 11. The measuring apparatus asclaimed in claim 10, wherein said conductive path traverses that oneflexure of each of said first and second pairs disposed closest to saidlink means.
 12. The measuring apparatus as claimed in claim 11, whereinsaid conductive path has a centerpoint and there is further includedmeans for connecting said centerpoint to ground.
 13. The measuringapparatus as claimed in claim 12, wherein said connecting meanscomprises a second conductive path extending along said support meansand said pivot flexure to said frame.
 14. The measuring apparatus asclaimed in claim 10, wherein there is included a second, referenceconductive path having a length equal to that of said first mentionedconductive path.
 15. Apparatus for measuring the specific force andangular rotation rate of a moving body, comprising:a) a monolithicsubstrate having first and second substantially planar surfaces disposedsubstantially parallel to each other; b) a first accelerometer formed ofsaid substrate and having a first force sensing axis for producing afirst output signal indicative of the acceleration of the moving bodyalong said first force sensing axis, said first accelerometer having aproof mass, a support frame, and at least one flexure connecting saidproof mass to said support frame; c) a second accelerometer formed ofsaid substrate and having a second force sensing axis for producing asecond output signal indicative of the acceleration of the moving bodyalong said second force sensing axis, said second accelerometer having aproof mass, a support frame, and at least one flexure connecting saidproof mass to said support frame; d) a dither frame formed of saidsubstrate, said dither frame being of a rectangular configuration havingfirst and third opposing members and second and fourth opposing members;e) a first pair of S-bend flexures connected between said support frameof said first accelerometer and said dither frame, and a second pair ofS-bend flexures connected between said support frame of said secondaccelerometer and said dither frame, said S-bend flexures being formedof said substrate for mounting said first and second accelerometers suchthat said first and second force sensing axes are both oriented at thesame angle with respect to said first and second surfaces and such thatsaid first and second accelerometers can be moved along a vibration axisperpendicular to each of said first and second sensing axes; f) linkmeans having first and second points connected respectively to saidfirst and second accelerometers and a pivoting point disposed a radiallength from each of said first and second connected points, supportmeans for mounting said pivoting point on one of said first and thirdmembers of said frame to permit said link means to pivot about saidpivoting point and when one of said first accelerometers if moved, toimpart an equal and opposite motion to said other of said first andsecond accelerometers, each flexure of said first and second pairs forproviding an effective radius of a length equal to that of said radiallength of said link means; g) drive means coupled to each of said firstand second accelerometers for imparting a dithering motion thereto of apredetermined frequency along said vibration axis; and h) said substratehaving a rate axis perpendicular to each of said first and second forcesensing axes and said vibration axis, whereby said first and secondoutput signals have a Coriolis component indicative of the angularrotation of the moving body about said rate axis.
 16. The measuringapparatus as claimed in claim 15, wherein each of said first and secondaccelerometers has a rectangular configuration including first and thirdopposing peripheral edges, and second and fourth opposing peripheraledges, said first and second pairs of flexures being connectedrespectively to said third and first peripheral edges of said first andsecond accelerometers such that each of their first and third opposingperipheral edges move substantially parallel with respect to said firstand third opposing members of said dither frame.
 17. Apparatus formeasuring the specific force and angular rotation rate of a moving body,comprising:a) a monolithic substrate having first and secondsubstantially planar surfaces disposed substantially parallel to eachother; b) a first accelerometer formed of said substrate and having afirst force sensing axis for producing a first output signal indicativeof the acceleration of the moving body along said first force sensingaxis, said first accelerometer having a proof mass, a support frame, andat least one flexure connecting said proof mass to said support frame;c) a second accelerometer formed of said substrate and having a secondforce sensing axis for producing a second output signal indicative ofthe acceleration of the moving body along said second force sensingaxis, said second accelerometer having a proof mass, a support frame,and at least one flexure connecting said proof mass to said supportframe; d) a dither frame formed of said substrate; e) a first pair offlexures connected between said support frame of S-bend said firstaccelerometer and said dither frame, and a second pair of S-bendflexures connected between said support frame of said secondaccelerometer and said dither frame, said flexures being formed of saidsubstrate for mounting said first and second accelerometers such thatsaid first and second force sensing axes are both oriented at the sameangle with respect to said first and second surfaces and such that saidfirst and second accelerometers can be moved along a vibration axisperpendicular to each of said first and second sensing axes; f) linkmeans having first and second points connected respectively to saidfirst and second accelerometers, a pivoting point disposed intermediatebetween said first and second connected points, and support means foraffixedly disposing said pivot point with respect to said frame topermit said link means to pivot thereabout and, when one of said firstand second accelerometers is moved, to impart an equal and oppositemotion to said other of said first and second accelerometers. h) saidsubstrate having a rate axis perpendicular to each of said first andsecond force sensing axes and said vibration axis.
 18. The measuringapparatus as claimed in claim 17, wherein said support means comprises apivot flexure comprising said pivot point.
 19. The measuring apparatusas claimed in claim 18, wherein said pivot flexure has a length andcross-sectional dimensions such that said flexure flexes with a simplebend.
 20. The measuring apparatus as claimed in claim 19, wherein saidlink means comprises first and second arms and a U-shaped memberdisposed there between and interconnecting said first and second arms,said pivot flexure having a distal end connected to said U-shapedmember, whereby said pivot point is aligned with said first and secondarms extending therefrom in radial fashion.
 21. The measuring apparatusas claimed in claim 17, wherein there is included first and secondconnecting flexures for respectively connecting said first and secondpoints of said link means to said first and second accelerometers. 22.The measuring apparatus as claimed in claim 21, wherein each of saidfirst and second connecting flexures have a length and cross-sectionaldimensions selected such that each of said first and second connectingflexures flex with approximately 50% simple and 50% "S-bend" movements.23. The measuring apparatus as claimed in claim 17, wherein a conductivepath is disposed on one of said first and second surfaces to traversesaid first and second accelerometers.
 24. The measuring apparatus asclaimed in claim 23, wherein said conductive path extends across oneflexure of each of said first and second pairs and across said linkmeans.
 25. The measuring apparatus as claimed in claim 24, wherein thereis included signal generator means for producing and applying a periodicdrive signal having a predetermined frequency to said conductive path,and magnetic flux producing means for producing and directing a magneticflux to cross said conductive path, whereby the interaction of saidmagnetic flux and said drive signal passing through said conductive pathcause said first and second accelerometers to vibrate along saidvibration axis at said pre-determined frequency.
 26. The measuringapparatus as claimed in claim 25, wherein said conductive path traversesthat one flexure of each of said first and second pairs disposed closestto said link means.
 27. The measuring apparatus as claimed in claim 17,wherein each of said first and second accelerometers has a rectangularconfiguration including first and third opposing peripheral edges, andsecond and fourth opposing peripheral edges, said first and second pairsof flexures being connected respectively to said third and firstperipheral edges of said first and second accelerometers such that eachof their first and third opposing peripheral edges move substantiallyparallel with respect to first and second opposing members of saiddither frame.